TRANSACTIONS OF THE SECTIONS. 213 



do not think political wisdom wiU ever lose any of its value, I think it only a part of 

 tliat political -wisdom to recognize that in such communities as ours tlie spread of 

 natural science is of far more immediate urgency than any other secondary study. 

 Whatever else he may know, viewed in the light' of modern necessities, a man who 

 is not fairly -\ersed in exact science is only a half-educated man ; and if he has sub- 

 stituted literature and history for natural science, he has chosen the less useful 

 alternati^e. 



One of the obstacles to the spread of science, and to our national prosperity, then, 

 I take to be the undue preference given to literaiy over natural knowledge, and, in 

 particular, the sacrifice of mathematical to classical study in the secondary school. 

 If you ask me why I lay so much stress on mathematical teacliing, my answer is, 

 that we need to study natural science exactly and quantitatively, not merely to cram 

 our memory with the qualitative characters of a few phenomena. Now, if we are 

 to count, to measure, to weigh, or othermse to ascertain quantity, we are reaUy 

 practising arithmetic, geometry, and mechanics. If we can learn these more ad- 

 vantageously than by the orduiary course of mathematical study, we shall simply 

 change the form of that study without evading the thing. But in truth mathe- 

 matics are too well understood, and on the whole too sensibly taught, to admit of 

 any great subversions. Improvements in detaU, and in the selection of the most 

 useful branches for study, there is doubtless room for, and indeed these are being 

 daily made. The cliief faults I notice are in teaching algebra too late, and in 

 teachmg Euclid (so called) too early. I regard abstract geometry as a foolish 

 study, imless accompanied, and even to a certain extent preceded, by the practice 

 of linear drawing. This is too often neglected. Moreover, I do not consider that 

 what is called Euclid — I use this expression advisedly — is the best possible text- 

 book for abstract geometry. I doubt if Euclid, if we judge him bv the best Greek 

 text handed down to us, is suited to our modern requirements. "What we actually 

 use is not Euclid, but only isolated portions of his book, freely altered by Robert 

 Simson. _ In my opimon the omissions and alterations have deprived the book of aU 

 lifelike vigour and human interest, and have made it as dull to the mature reader 

 as it necessarilv is to the unfortunate boys whose first introduction to geometry it 

 too frequently forms. 



Apart from the general fault of giving too low a place to mathematical teacliing 

 (a great faidt, and one which we are only slowly mending) is our not paying suffi- 

 cient _ attention, and sufficiently early attention, to mechanical and geometrical 

 drawing. On this pomt I need add but little to what was said by Prof. Fleeming 

 Jejikin in his address to this Section at Edinburgh in 1871. That is possibly the 

 point on which we compare least favourably with neighbouring countries. One 

 important remark of his I am anxious to gi\e prominence to, and that is, that de- 

 scripti^-e geometry is not what is wanted. I fear, indeed, that many teachers of tins 

 subject have failed to realize its true meaning, and confuse it with the theory of 

 geometrical projection, of wliich it is in truth a development and extension, not a 

 particidar application. So far as the preliminary chapters of an elementary work 

 on it are concerned, the collision is natural and perhaps not ^erv material ; for all 

 that relates to the point and straight line is simply plan and elevation, and the plane 

 needs but little more. But the characteristic feature of descriptive geometry is due 

 to the fact that surfaces cannot (with the exception of cylindrical surfaces) be 

 represented by plan and elevation. They are therefore, in this science, indicated 

 by a general and systematic method, which, without representing them to the eye, 

 enables us to handle them geometrically, to find their intersections, their tangents, 

 and their shadows, with the same certainty as if we had models before us. So far 

 as points and lines, straight or curved, are concerned, it does not differ from geome- 

 trical projection ; the difference is, that it deals effectually with planes and curved 

 surfaces, which geometrical projection cannot do. To those who have to deal with 

 curved surfaces it is as important as linear drawing is to the student of plane o-eo- 

 metry, because models are practically unprocurable, and conception in three dimen- 

 sions is not easily got, except through descriptive geometry. But for ordinary 

 school purposes it is a very barren exercise. I state this advisedly, being thorouglily 

 familiar with both its use and abuse. A much more important exercise of geo- 

 metry^ and one more immediately useful, is the geometrical representation of arith- 



187*5. ly 



